Problem Solving

Hi,

I am having problem solving this question - could anyone explain??

Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 30%
(B) 33 1/3%
(C) 37 1/2%
(D) 40%
(E) 50%

Hi, I'm not sure if the following is the most efficient way to do it. At least for me it was quick to do this way!

in solution Y = 30% x + 70% w(ater)

So, in 8kg of Y = 2.4x + 5.6w

from this 2kg water is removed (Evaporated) so, in the remaining
6kg Y = 2.4x + 3.6w.

Now 2kg Y is added, which has 0.6x + 1.4w. So,

6kg Y = 2.4x + 3.6w.
2kg Y = 0.6x + 1.4w
-------------------------
8kg Y = 3.0x + 5.0 w

x = 3/8 * 100 = 37.5%

Answer is C

I normally solve such problems by making a table.

It very clear and I think quicket enough! Thank you!

solution Y contains 30% (i.e 0.3) liquid X and 70% (0.7) water.
8kg of solution Y will contain = 30% liquid X in 8kg + 70% water in 8kg
=0.3 (8) kg liquid + 0.7(8) kg water
= 2.4 kg liquid X + 5.6 kg of water
Now, if 2 kg water evaporates from 8 kg of Y, we have
= 2.4 kg liquid X + (5.6-2) kg of water left.
= 2.4 kg liquid X + 3.6 kg of water
=6 kg of Y

2 kg of Y will contain,
= 30% liquid X in 2 kg + 70% of water in 2 kg
=0.3(2) kg liquid X + 0.7(2) kg water
= 0.6 kg liquid X + 1.4 kg water
Adding this to the liquid we have left, we now have = (2.4 + 0.6) kg liquid X + (3.6+1.4) kg water
=3 kg liquid X + 5 kg water
=8 kg of liquid

percentage of liquid X= $$\frac{3kg}{8kg}\cdot100\%\ =\ 37\ \frac{1}{2}\%$$ .
Hence, the correct option is C